To begin with, we must recall that we have chosen to work in the exact alignment limit in this model. Thus, the CP-even scalars \(H_1\)  and \(H_2\)  have couplings to \(Z\)  (and \(W\) ) boson pairs exactly equal to zero. As such, experimental searches for extra scalar resonances decaying into \(Z\)  or \(W\)  boson pairs [1]}, [2]}, [3]} are automatically satisfied in our parameter scan. Deviations from the alignment limit to be considered in a more general analysis might somewhat change that state of affairs. Given how SM-like the 125 GeV scalar appears to be in the LHC measurements, the couplings of \(H_1\)  and \(H_2\)  to electroweak gauge bosons should always be heavily suppressed,
so we do not perform such more generic off-alignment analysis in the current work. However, the sum rule for scalar-gauge boson couplings – which in the exact alignment limit makes \(H_1\)  and \(H_2\)  gauge-phobic – does not apply to Yukawa interactions. For instance, in the 2HDM or in SUSY models, interactions of the pseudoscalar \(A\)  to fermion pairs may
be enhanced (or suppressed) by a factor of \(\tan \beta \) . A promising avenue in searches for additional scalars is therefore the di-tau channel, where the current and future LHC sensitivities may well reveal their presence.
